Question

Find the probability that a dart would land in the shaded region: 16 in 16 in 16 in 16 in

Answer 1

NoGiven:

The length of each side is 16in.

To find:

The probability that a dart would land in the shaded region.

Step-by-step explanation:

First, find the whole area.

`\begin{gathered} A=a^2 \\ =16^2 \\ A=256\text{ square inches} \end{gathered}`

Next, find the area of the shaded region.

`\begin{gathered} Shaded\text{ area = Whole area-unshaded area} \\ Area=Whole\text{ area-\lparen4}* Area\text{ of the quadrant\rparen} \\ A=256-4*(\pi r^2)/(4) \\ A=256-\pi r^2 \end{gathered}`

Substituting r = 8 we get,

`\begin{gathered} A=256-3.14(8^2) \\ A=256-200.96 \\ A=55.04\text{ square inches} \end{gathered}`

The probability is,

`\begin{gathered} P(E)=\frac{Area\text{ of the shaded region}}{Total\text{ area}} \\ =(55.06)/(256) \\ P(E)=(43)/(200) \\ (or) \\ =0.215 \end{gathered}`

Final answer:

The probability that a dart would land in the shaded region is,

`(43)/(200)\text{ \lparen or\rparen 0.215}`